x^2+11x+31=7

Solution for x^2+11x+31=7 equation:

Simplifying
x2 + 11x + 31 = 7

Reorder the terms:
31 + 11x + x2 = 7

Solving
31 + 11x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
31 + -7 + 11x + x2 = 7 + -7

Combine like terms: 31 + -7 = 24
24 + 11x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
24 + 11x + x2 = 0

Factor a trinomial.
(8 + x)(3 + x) = 0

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-8, -3}